A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place.
Where b = 28°

A)18.0 lb
B)17.0 lb
C)16.0 lb
D)19.0 lb
E)15.0 lb

Question

A traffic light weighing 16 pounds is suspended by two cables (see figure).Find the tension in each cable.Approximate the answer to one decimal place. ​​  ​
Where b = 28°
​
A)18.0 lb 
B)17.0 lb 
C)16.0 lb 
D)19.0 lb 
E)15.0 lb

Quizplus · Accepted Answer

We can use the equations for static equilibrium to solve for the tensions in the cables. Let T1 and T2 be the tensions in the cables, and let the weight of the traffic light be W=16 lbs. Then, we have:

ΣF_x = 0: T1*cos(b) - T2*cos(b) = 0
ΣF_y = 0: T1*sin(b) + T2*sin(b) - W = 0

Simplifying the first equation gives T1 = T2. Substituting this into the second equation and solving for T1 or T2, we get:

T1 = T2 = W/(2*sin(b)) = 16/(2*sin(28)) ≈ 17.0 lbs

Therefore the best choice is B, which is the closest answer to the calculated tension in pounds.

A Traffic Light Weighing 16 Pounds Is Suspended by Two